We show that eigenvector decomposition can be used to extract a term taxonomy from a given collection of text documents. So far, methods based on eigenvector decomposition, such as latent semantic indexing (LSI) or principal component analysis (PCA), were only known to be useful for extracting symmetric relations between terms. We give a precise mathematical criterion for distinguishing between four kinds of relations of a given pair of terms of a given collection: unrelated (car - fruit), symmetrically related (car - automobile), asymmetrically related with the first term being more specific than the second (banana - fruit), and asymmetrically related in the other direction (fruit - banana). We give theoretical evidence for the soundness of our criterion, by showing that in a simplified mathematical model the criterion does the apparently right thing. We applied our scheme to the reconstruction of a selected part of the open directory project (ODP) hierarchy, with promising results.